You are camping in the wilderness. After a few days, you are horrified to discover that you did not pack as many batteries as yo

Q should be positioned 4.8 miles east of point B. Explanation: From the diagram, we can define the construction cost as a function of angle θ (as illustrated). The underwater pipe length (marked in blue) equals 6/cos θ, while the land pipe length (marked in brown) is (8 - 6*tan θ). The total construction cost formula is: Construction Cost = (6/cos θ)(6000) + (8 - 6*tan θ)(3750). This formula is represented in terms of θ, which can vary from 0 degrees to 53.13 degrees according to the diagram. To find the angle θ that minimizes the construction cost, we differentiate the Construction Cost function with respect to θ and set it to zero. The derivative yields: -4500(5*sec θ – 8*tan θ)(sec θ) = 0, leading to θ = 38.68 degrees. By substituting θ, we can determine the distance of Q from B, which equals 6*tan θ. This calculates to a distance of 4.8 miles.

Answer:

a

The value at a point inside is Zero

b

The electric field is

Explanation:

We know from the problem that

The charge magnitude is

The radius of the spherical ball is

According to Gauss’s law, the enclosed charge within a conductor is zero which indicates that the electric field within the spherical ball is zero

On the outside, the electric field around the spherical ball is mathematically expressed as

Here a denotes a point outside the spherical ball with its value of

and k represents Coulomb's constant, valued at

=>

=>

Answer:

F = 0.535 N

Explanation:

We will apply energy concepts, considering both the peak and the bottom of the path.

Top

   Em₀ = U = mg y

Bottom

    = K = ½ m v²

    Emo =

    mg y = ½ m v²

    v = √ (2gy)

   y = L - L cos θ

  v = √ (2g L (1 - cos θ))

Next, we will employ Newton's second law at the lowest point where the acceleration is centripetal.

     F = ma

     a = v² / r

For the turning radius, the cable length is r = L.

    F = m 2g (1 - cos θ)

Now, let's find the result.

    F = 2  1.25  9.8 (1 - cos 12)

    F = 0.535 N

   

Answer:

x = v₀ cos θ   t,   y = y₀ + v₀ sin θ t - ½ g t2

Explanation:

This pertains to a projectile motion scenario. Here, we will express the equations for both the x and y dimensions.

Now, we will apply trigonometry to determine the initial velocity components.

              sin θ = / v₀

              cos θ = v₀ₓ / v₀

              v_{y} = v_{oy} sin θ

              v₀ₓ = v₀ cos θ

Next, let's formulate the equations of motion.

X axis

         x = v₀ₓ t

         x = v₀ cos θ   t

        vₓ = v₀ cos θ

Y axis

        y = y₀ + t - ½ g t2

        y = y₀ + v₀ sin θ t - ½ g t2

        v_{y} = v₀ - g t

       v_{y} = v₀  sin θ - gt

        = v_{oy}^2 sin² θ - 2 g y

It is evident that the major distinction lies in the fact that in an inclined launch compared to a horizontal one, the velocity comprises different components

Response:

Clarification:

Impulse is equal to change in momentum

mv - mu, where v and u represent the final and initial velocities during the surface impact

For the downward motion of the baseball

v² = u² + 2gh₁

= 2 x 9.8 x 2.25

v = 6.64 m / s

This becomes the initial velocity upon impact.

For the upward movement

v² = u² - 2gh₂

u² = 2 x 9.8 x 1.38

u = 5.2 m / s

This becomes the final velocity post-impact

change in momentum is

m ( final velocity - initial velocity )

.49 ( 5.2 - 6.64 )

=.7056 N.s.

Impulse exerted by the floor in the upward direction is

=.7056 N.s